The PLC's will keep on talking to one another, and any HMI devices, and any other automation hardware they're connected to.
What's going to happen is that whatever PC software on your workstation that is using RSLinx won't be able to use it anymore if you force it to shut down.
So RSLogix would time out and go offline, or RSView would stop displaying live data, or even FactoryTalk Transaction Manager might stop storing historical data into SQL.
But shutting down RSLinx doesn't interrupt the PLC networks or operation.